Show HN: Scroll through all 43252003274489856000 Rubik's Cube states | Hacker News Reader

Show HN: Scroll through all 43252003274489856000 Rubik's Cube states

everycube.alen.is

295 pointsAlen123122 comments

I wrote a 3d rubiks cube slot machine for my old online casino. It scrambled the cube randomly 4 times and gave the player 60 seconds to solve it by twisting up to 3 times. Lots of weird quaternion math to handle the spinning and shift key twisting at the same time. All with simple geometry in Away3D / AS3.

The real hard part of designing that game was creating the payout structure. The game paid an equal amount for each "line" of 3 colors in a row on any face after the player made their third move. There was a progressive take and jackpot for a perfect solution. And I specifically wanted to target a zero house edge for the game, to reward the best problem solvers. So the question was, given 4 random twists off a perfect cube, what are the individual chances of getting 64, 63, 62...1 lines of sequential color given the best 3 spins from the initial random state, and then hiw to allocate the payout structure accordingly.

Probably a billion monte carlo runs and I had a pay table. It was lots of fun. I wish more gambling games rewarded skill that way.

Casino games are rarely zero house edge. Is there a way you signaled this feature to problem solvers? Did the game prove to be successful?

it could be a video game with no real money, and some online casinos have zero edge games where you pay a small fee when you win.

any time there is skill in an online casino game where money is involved, there is cheating too

Just change the parity by swapping two stickers on a corner piece, and no amount of skill can solve it.

Experienced cubers will catch on very quickly, the really good ones would notice it on sight.

There are laws about making casino games impossible to win, so a game that is transparently in violation wouldn't last long.

Plus this would seemingly violate compliance with laws protecting disabled people. For instance, someone with mobility issues might know the solution but wouldn't be able to hit the buttons in time.

By that logic, wouldn’t prizes in “test of strength hammer” games also be illegal?

The game just has multiple aspects to it.

Sweet, can I mint these as NFTs? I don't know how to multiply 43252003274489856000 by 50 USD but I think it could make me a lot of money, and I like money.

That's more money than there is in the universe, I think you're onto a winner here!

If we can capture even 1% of the market…

You only need to sell one at $50, then market cap does the rest and you are boundlessly rich.

And then countless politicians will blame you for not paying for everything out of your market cap.

More like countless CEOs will claim that having to pay taxes on that wealth will destroy society, despite no jobs being created to make the product and the product itself have zero value to society.

Well yes, you shouldn't pay tax on that, and it would cause huge problems. If your house increases in theoretical value should you pay tax on the increase? Or only when you sell the house?

> If your house increases in theoretical value should you pay tax on the increase?

You do understand this is exactly how property taxes work, right?

Yes I want to be a billionaire when it comes to:

* Public image

* Borrowing power

* Atttacting investors

But a pawper when it comes to:

* Paying tax

Then why do they pay so much tax? Top 1% pay 50% of the tax or whatever, and some of that other 50% of tax is actually just the public sector paying tax back, it's not a net contribution.

Well top 1% make most of the money so that makes sense. Need deeper analysis. What about top 0.01%?

The other 50%... those people are working!!!! Can't avoid paying people unless we go back to slavery.

Regardless it is one of the rich tricks to borrow against unrealized gains. And other shenanigans.

In case someone is curious, NFTs were tradeable tokens popular for a short while in the early 2020s.

> Initially pitched in 2017 as a new class of investment asset, NFT trading increased from US$82 million in 2020 to US$17 billion in 2021. Its market was occasionally compared to an economic bubble or a Ponzi scheme. In 2022, the NFT market collapsed; a May 2022 estimate was that the number of sales was down over 90% compared to 2021. By September 2023 one report claimed that over 95% of NFT collections had zero monetary value.

https://en.wikipedia.org/wiki/Non-fungible_token

The reason NFTs "failed" is that the "assets" were jpegs with infinitesimal intrinsic value(pre–ai slop) and even less market appeal.

We have people wasting money on jpegs and people wanting to own things outside of game inventory screens even today. Something akin to NFTs could still become a part of the economy.

Define intrinsic value in a measurable way that does not depend on any specific human’s subjective estimation.

How many calories do you get when you eat it or burn it. Everything else is down to taste.

Is it useful? If not, it has no intrinsic value. It might have emotional value, either by being a memento, something of historical significance..., or something to calm the the dreams for quick, easy, and abundant money.

Define useful in a measurable way that does not depend on any specific human’s subjective estimation.

Is a dictionary definition insuficient?

useful

- Having a beneficial use; serviceable: "a useful kitchen gadget."

- Being of practical use: "a useful job; useful members of society."

- Full of use, advantage, or profit; producing, or having power to produce, good; serviceable for any end or object; helpful toward advancing any purpose; beneficial; profitable; advantageous: "vessels and instruments useful in a family; books useful for improvement; useful knowledge; useful arts"

Let’s say I bought an NFT for X and later sold it for Y profit. I bought a house with Y. The person who received X bought a car with it, or maybe long in oil futures with X before the Iran war, made Z, and bought a field with the profit. Or maybe he put Z in a couple of bonds and used the resulting return later.

I'd say that's a scam, not an argument for the usefulness of NFTs. My counterargument is that most NFTs made people lose money instead of buying them houses or oil fields.

I'd bet that most stories of NFTs translating to material wealth come from minters or the inner circle of early adopters, because they made something useless and valueless, and somehow convinced enough people that it was worth buying it for hard-earned cash. Many lost so a few could make bank.

They convinced fools to enter a rigged gamble.

Value and usefulness are again subjective. For instance, what value would you have put on a can of Piero Manzoni’s Artist’s Shit? After all, we could all take a shit in a can. One can was sold for 124k EUR.

Many people lost some money. Maybe they gained from the experience. Many people made money. Maybe they lost some on other things. Many people got their knickers in a twist over things with such perceived (by themselves) low value selling for high value. Maybe they forgot that fiat money is a construction as well. Conversely, maybe they gained something intangible from the whole experience.

https://en.wikipedia.org/wiki/Artist's_Shit?wprov=sfti1

This was a core point of Zen and the Art of Motorcycle Maintenance. Per that book you are asking for the impossible.

Cryptopunks are still over $60k. Pricy jpegs.

Let me guess, that's crypto value, because no one in their sane mind would pay $60K in real money for crude, combinational images. I hope this, and Bored Ape Yacht Club still exist many years in the future, just to remind our descendants of the things we burned the planet for.

Often the actual token would just hold a link to a jpeg. With all the consequences of link rot.

The assets were the expected future value of worthless items in an engineered bubble.

The bubble never inflated, so the nominal value crashed back down to the real value almost immediately.

Fairly sure there was some money laundering happening too.

> We have people wasting money on jpegs and people wanting to own things outside of game inventory screens even today. Something akin to NFTs could still become a part of the economy.

Horrible comparison, because people buying hats or reskins, let alone unique game items, are actually enjoying their purchases before the game is sunsetted and it all dissolves into the digital IP void. NFTs offer no value besides moral ownership; if Capitalism and Greed could make jokes, NFTs would be among their best.

It's funny to think that if bitcoin was backed by jpegs it would've failed already.

Donald, is that you?

lol!

Joke's on you, I'm going to do the same thing but only charge $5. Sucker!

My scroll wheel covers about 12 states per inch of travel. Did the stubby pencil work and it would take about 9.5 years to scroll through them all if the wheel surface was moving at the speed of light.

Auto rotate and auto scrolling would be neat.

Edit: also 2D https://www.github.com/AdamWhiteHat/RubiksCubeControlWpf

I clicked the button on my Logitech M720 mouse to free spin, spun the wheel like I was on the Price is Right, and got to 791,001!

Love my Logitech free-wheeling mouse wheels! Not having a heavy wheel and detent-free option is a non-starter for me.

791K? Those are rookie numbers. Get yourself a can of compressed air and you'll be pushing millions.

This is a nice visualization. Are there any keyboard keys to just advance one position along the line? I tried the arrow keys but they jumped quite far.

I don't know how this was generated (BFS and flattening?) it seems adjacent indices aren't just one move apart ... but they could be!

There is a Hamiltonian circuit for Rubik's cube: https://bruce.cubing.net/ham333/rubikhamiltonexplanation.htm...

Following the circuit would be like Gray codes instead of binary digits. You only flip one bit at a time when going to the next number.

You can change the jump-amount in the top right. (500 was an odd default).

For me that step-size only works to affect the jumps given by the mouse scroll wheel. The keyboard arrow keys (Left and Down) also seem to do some scrolling after you have selected the number line. However, both arrows produce steps in the decreasing direction.

The difference between two successive steps by pressing a key seems to be 86504006548979

Reminds me of a book I recently read:

https://en.wikipedia.org/wiki/A_Short_Stay_in_Hell

The numbers produced by permutations are astounding! Especially compared to the (much smaller) numbers in our actual physical universe.

My favorite one is chess games. If you managed to compress each chess game down to just a single atom, the physical size of a disk to save this data would exceed the amount of atoms in the universe. Even the number of theoretic positions (ignoring legality/possibility) is just below the number of atoms in the universe.

Though it must be said that once one starts looking at permutations of things, the number of atoms in the universe seems quite small indeed. 10^80? What's that, like 7 or 8?

The number of permutations of n distinct objects is n!. So, probably a bit more than 8, since 8! < 10⁸, but I don’t think you are terribly off :-)

Edit: 58! < 10⁸⁰ < 59!

Ah nice, it has some of my favourites!

I am very curious about your other favorites it does but have.

My kids had a science battle in the basement last summer, which resulted in both their Rubik’s Cubes colliding mid air. They both exploded (the cubes, not the kids) and were reassembled at a “fix this before mom finds us” rush speed.

I think my favourite is this pattern my 9 year old makes on “Greeny” (that’s his pet name for the cube that now has 11 green squares) where all four top corners are red/white/blue.

This here is the difference between theory and practice. Our minds are to feeble to understand reality.

When I was a kid (many, many moons ago) I found a solved Rubik's Cube in a house where we were staying. I played with it and soon enough couldn't put it back in its solved state.

So I took it apart and rebuilt it 'properly', which didn't take long and wasn't too hard. I wonder how many people did the same.

My kid wanted to jump 3x3x3 and go directly to a 4 cube. I freaked out when we messed it and thought we could never solve it, because you can't disassemble a 4 cube into pieces like a 3 one. In the end it's not so difficult: like a 3 as you move around the two middle pieces of each edge together like one.

Reminds me of that time when, as an undergraduate, my "team" entered a Problem Solving Competition and couldn't choose one of the two problems so we did both in parallel.

One of us wrote a program in BASIC on a Tandy 1000 that the rest of us estimated would take more than a google years to finish, but he wasn't be dissuaded and let it run the whole weekend.

I made an analysis that was mostly correct but was off by a factor of four because I mistook a radius for a diameter.

I think the number is spelled googol.

Yeah

https://en.wikipedia.org/wiki/Googol

This is pretty cool. Same concept (and I would assume implementation) as https://everyuuid.com/

Implementation details can be found here: https://eieio.games/blog/writing-down-every-uuid/

It took Ernő Rubik four years to develop the cube.

He immediately scrambled it, then spent the next month figuring out if it could be solved.

Luckily no one told him there were 43 quintillion valid combinations.

Solved theoretically? I figure you could at least intuit that reversing all the moves in the scramble in reverse order would solve it.

The above makes everything sound very intentionally done towards the end result. He came about making the cube for finding ways to tackle the engineering challenge of building a device which moves in such levels if freedom, ended up scrambling it, and then spent a month figuring out how to treat the scrambled state as a puzzle to be solved. Messing with it gave him insight into just how complex a puzzle it was and the rest goes from there.

He spent the next month coming up with an algorithm to solve it, not knowing if such an algorithm was even possible.

After he sold the puzzle, he traveled around to various conferences, to prove it could be solved.

The color interpolation in 2D mode is bad. Instead of interpolating through RGB, you should use OKLCH

Demo: https://jsfiddle.net/t80eLfc2/2/

Interpolating in RGB just uses linear interpolation on each channel, so it ends up passing through grey in a lot of cases, and the colors look very desatured.

Interpolating in OKLCH preserves chroma and instead passes through different hues.

I used the "FX" option and I think there's a bug. The center tiles on each side always stay in the same position.

On a Rubiks cube, the center tile always remains constant. I was surprised at this when I accidentally broke one apart to find a static 3d cross piece to each cube face (e.g. a non-moving tile). Everything else rotates around it

The center tiles on a Rubik's cube don't move, they only rotate in place.

I think you thought a /s can be sometimes implied in HN comments

I came to this comment because I was also thinking that this was a bug. Interesting to know this is by design.

Reminds me of https://everyuuid.com/

Maybe show the minimum number of moves required to solve each state :)

And maybe sort them by "distance to solved".

I love this. Excellent weird internet thing.

Wow, this was really fun to play around with! Amazing execution and launch!

Quick feedback: it’d be great if the page updated when the URL changes, so you can explore different positions without reloading.

Right now, if I change the URL/hash of the cube position (eg: incrementing by 1 https://everycube.alen.is/?view=3d#5319001606686939024 ), the app doesn’t update and I have to open the new URL in a separate tab to see the new position. [Chrome 150 on Mac OS X 10.15.7]

just shipped a fix, the app now listens for hash/URL changes and updates the view without needing a reload. thanks for catching this!

Anyone else surprised how small the number is? It looks quite big without commas but if you add them in it looks like the sort of number that is almost conceivable 43,252,003,274,489,856,000 43 quintillion, that's the type of number i've vaguely heard of. Compared to the number of possibilities for a shuffled deck of cards 80,658,175,170,943,878,571,660,636,856,403,766,975,289,505,440,883,277,804,000,000,000,000 Thats a big number, and weirdly I think those 00s at the end are exact not a rounding error.

It felt pretty big to me, considering Rubik's cubes only have 26 pieces, their valid slots are not all the same, and some of their states are mirrored.

It's really 21, since the centers are all one unmovable piece.

https://jhodileongseportfolio.weebly.com/center-faces.html

Good catch, forgot about that.

And yet sorting a deck of cards is much easier than solving the cube.

43,252,003,274,489,856,000 is a fun trivia number, but it tells you nothing about how hard it is to solve the cube.

Current speed cube record appears to be 2.76s.

Has anyone ever sorted a randomly shuffled deck of cards in under 3 seconds?

The number of permutations is 52! which is 1x2x3...x51x52

So, at some point you're going to be multiplying by 10, 20, 30 etc. Plus you'll have 2x5x.., 4x50x... (if you rearrange the terms). It therefore makes sense that you'll end up with a bunch of zeros on the end.

In fact that means the largest factorial that doesn't end in 0 must be 4! because you could always move the ...x2x5 to the end of the series.

There are 43,252,003,274,489,856,000 (~4.3 × 10¹⁹) different positions. 1. If I try every position (1 position/sec) knowing it's unique, it will take me 1.37 trillion years. 2. If the pro tries (let's say 10 positions/sec), it will take 137 billion years. The universe is younger than that. :-D

Wondering how fast the machine or computer will do that?

Here is another way of looking at the same question:

https://news.ycombinator.com/item?id=49252106

Wouldn't it be cool to click and then see the quickest solution and it rotates in front of you, or a sequence of moves to solve.

The moves are reversed? i.e., F is F'

https://everycube.alen.is/?view=3d&alg=R%20U%20R%27%20U%27

Should be:

https://alg.cubing.net/?alg=R_U_R-_U-

Ah great, so now I've got the choice to "Complete he Rubik's cube"... it'll just take 432520032 times as long as completing today's Instagram...

First thought; this could be turned into a really cool password generator

OK. So I put the slider into a random middle location. Then I zipped it back all the way left as fast as I could. Still not up to competitive speed cubing level! Shucks, golly, gee.

> Application error: a client-side exception has occurred (see the browser console for more information).

On ios Firefox and Safari unfortunately, would love to see this site

Application error: a client-side exception has occurred (see the browser console for more information).

iPhone; Safari; Lockdown mode.

Exponential growth is always mind boggling! Crazy to think there are that many states.

What's the correct way to sort a Rubik's Cube state?

this does permutations of pieces position and orientation

would be cool permutations of moves instead...the visuals would be especially interesting to have as a raw Rubik's simulator

well that's just like, your coordinate system, man

This is very satisfying to play with, top work!

Is your mercor.com site works really?

structure emerges from chaos at 23,738,673,083,197,685,761 & 34,677,398,788,068,093,945

True! How did you spot this though? Did you look at every possible position?!?

I bet they entered the scramble U2 D2 R2 L2 F2 B2 or something to that effect. My 9yo loves this pattern.

user mlni is right. I can solve a cube IRL, and these patterns are easily derivable from the solved state with only a few twists. There is an R' button in the upper right that let's the user enter scramble commands, so I manually entered them, and landed on these Permutation IDs.

Excellent! Thanks for the info!

Took me a hell of a lot more moves than that (30 septendecillion) for structure to emerge from chaos with paperclips.

https://en.wikipedia.org/wiki/Universal_Paperclips

https://www.decisionproblem.com/paperclips/index2.html

  Universal Paperclips
  • a game by Frank Lantz
  • combat programming by Bennett Foddy
  'Riversong' by Tonto's Expanding Headband used by kind permission of Malcolm Cecil
  > © 2017 Everybody House Games I

  Paperclips: 30,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000

But, why?

literally doom scrolling

haha healthiest possible doom scroll though

Cool!

At some point though, how many states is too many?

We have massive housing affordability and employment shortage problems, meanwhile here’s a tech elite flouting 4x10^9 states which he doesn’t pay taxes on and most of them will not even get used. Is that really fair?

It's actually about 4x10^19 (exponent 19, not 9).

Typo, but this just shows the extreme inequity when one cube amasses so many states.

Imagine being so well off that you don't even notice being off by ten orders of magnitude. Meanwhile, there are people dealing with negative exponents.

I think you missed at least a few, can you re-check through them?

cool!

It would be really funny, and sociopathic, if every state change registered as a browser history entry so I had to click Back 50,000 times to get back to Hacker News.

Oh wow, you don’t do “Open in New Tab” when reading HN? Thanks for the idea, I should really try that, maybe it will help with my infinite open tabs problem.

nice, now sort the list in some interesting way

Non-AI posts be like

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